Pure resolutions of vector bundles on complex projective spaces
Algebraic Geometry
2012-10-31 v1
Abstract
We prove three results on pure resolutions of vector bundles on projective spaces. First, we show that there are simple vector bundles of rank n on Pn with arbitrary homological dimension. We then analyze the pure resolutions given by the sheafification of the Koszul complex of a certain algebra and by the sheafification of the minimal free resolution of a compressed Gorenstein Artinian graded algebra, proving that their syzygies are simple vector bundles. Our main tool is a result originally established by Brambilla, for which we give an alternative proof using representations of quivers.
Cite
@article{arxiv.1210.7835,
title = {Pure resolutions of vector bundles on complex projective spaces},
author = {Marcos Jardim and Daniela Moura Prata},
journal= {arXiv preprint arXiv:1210.7835},
year = {2012}
}
Comments
27 pages. Part of the second named author's PhD thesis